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Demographics | Physical health | Hearing | Cognition | Mobility and balance | Quality of life | Mental health | Social participation and support | Views on hearing loss |


Background

Why impute missing data?

Logistic regression and other statistical methods require complete cases. In our case, with 40+ variables of interest, dropping participants with any missing values leads to a sample size of 200+ cases instead of 500+. There is loss of power, and estimates from models will likely be biased. The goal of missing data imputation is to restore variance of the sample to make it better reflect characteristics of the population (i.e., give accurate estimates of standard errors, CI’s, and p-values).

MICE procedure

‘Multiple Imputation by Chained Equations’

  1. Say there are three variables ‘A’, ‘B’, and ‘C’, each with some missing values. Choose variable ‘A’ to start filling in. Fill in missing values in ‘B’ and ‘C’ with temporary values, such as the mean.

  2. Make an equation A ~ B + C, using observed cases of ‘A’ to predict missing values of ‘A’, including a random component. Move on to predicting missing ‘B’, using B ~ A + C and including predicted ‘A’, again including a random component. Move on to predicting missing ‘C’, using C ~ A + B and predicted ‘A’ and ‘B’. This is one cycle.

  3. Choose the number of cycles, say 10 iterations. At the end of 10 iterations, an “imputed” dataset is formed with no missing values. Choose the number of imputed datasets to form (the same analysis will be conducted on each slightly different dataset, and the results will be pooled). Choose which variables should be used as predictors of other variables. Choose which method to use for predicting missing values, e.g., predictive mean matching. For derived variables such as summed scores, consider whether to impute components first and then calculate derived scores, or impute derived scores. Consider whether there should be an order of which variables to start imputing first.

  4. Check whether the imputed data “converge” (the means and SEs stabilize after a few iterations, and are similar across imputed datasets). Check the distributions and characteristics of imputed data (e.g. integer-only values, floors and ceilings, plausibility), and their similarity to observed data.


1. Pre-imputation work

(i) Evaluate missingness

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Variables of interest Demographics: Age, Gender, Work, Volunteer, Live alone
Physical health: Rating, Multimorbidity score, Subjective vision (loss, rating aided), Subjective hearing (loss, rating aided, rating unaided)
Hearing health: Hearing device use, Hearing device type, Tinnitus past 7 days, 15i-SSQ mean score, SIM mean score, EmoCheQ mean score, HHIE-S total score, BPTA4
Cognitive health: Subjective cognitive impairment, CSRQ mean score
Mobility and balance: Mobility aid use, ABC (balance confidence) mean score
Quality of life: SWLS mean score, WHO overall QoL, WHO health QoL, WHO money, WHO four domains
Mental health: PHQ4, split into anxiety and depression subscores
Social factors: Loneliness, Social Network Index, Social Participation Frequency, Social Participation Types, Social Support MOS mean score
Views: Connections total correct score, Motivations mean score
% Missing data within participants
## 
##   The decimal point is at the |
## 
##    0 | 00004444444444444444444444444444444444444999999999999999999999999999+193
##    2 | 22222222222222222222222222222222222222222277777777777777777777777777+16
##    4 | 000044444999993333333888888888888
##    6 | 222222222222222666666666666666666111111111111111111155555555555
##    8 | 0000000004444888833337777
##   10 | 221199
##   12 | 488
##   14 | 2055
##   16 | 47
##   18 | 65
##   20 | 
##   22 | 5
##   24 | 2
##   26 | 
##   28 | 
##   30 | 
##   32 | 
##   34 | 
##   36 | 
##   38 | 
##   40 | 
##   42 | 9
##   44 | 
##   46 | 
##   48 | 
##   50 | 
##   52 | 
##   54 | 
##   56 | 
##   58 | 
##   60 | 6
##   62 | 
##   64 | 6
##   66 | 87
##   68 | 
##   70 | 8827
##   72 | 6
##   74 | 337
##   76 | 0
##   78 | 
##   80 | 5
##   82 | 
##   84 | 
##   86 | 
##   88 | 
##   90 | 6
##   92 | 
##   94 | 
##   96 | 
##   98 | 66
Missing data patterns


Participants with <26% missing data (n=509):


Participants with >42% missing data (n=18):


(ii) Data cleaning

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Rules
  • For “single-item” variables (e.g. loneliness): NA’s are left as is.
  • For co-morbidity checklist: All responses other than “yes” (NA’s, No, Don’t know) are treated as “no”.
  • For composite variables: If a participant has “NA” for all items, the composite score is also “NA”.
  • WHOQOL-BREF: Follow their protocol for NA’s.
  • For SIM, EmoCheQ, CSRQ, PHQ4, Views on motivations: Impute case mean.
  • For 15i-SSQ: Impute case mean within subscale.
  • For HHIES: Impute case mode within subscale.
  • For ABC: Recode NA’s to 0 (single participant).
  • For Social Network Index: Recode NA’s to “never”.
  • For Social Participation: Recode NA’s to “never”.
  • For Social Support: Recode NA’s to “none”.
  • For Views (Connections): Drop foil item; only correct items credited.
  • For Views (Motivations): Impute mean.


Cleaning details


(iii) Evaluate missingness again

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% Missing data within participants
## 
##   The decimal point is at the |
## 
##    0 | 00000000000000000000000000000000000000000000000000000000000000000000+151
##    2 | 22222222222222222222222222222222222222222222222222222222222222222222+51
##    4 | 333333333333333333333333333333333333333333333
##    6 | 555555555555555555555555555555555555555555555555555555555
##    8 | 777777777777777777777777777
##   10 | 99999999999
##   12 | 00000
##   14 | 
##   16 | 4
##   18 | 6
##   20 | 
##   22 | 
##   24 | 
##   26 | 
##   28 | 
##   30 | 
##   32 | 
##   34 | 
##   36 | 
##   38 | 
##   40 | 3
##   42 | 
##   44 | 
##   46 | 
##   48 | 
##   50 | 0
##   52 | 22
##   54 | 3
##   56 | 
##   58 | 7777
##   60 | 999
##   62 | 
##   64 | 2
##   66 | 
##   68 | 6
##   70 | 7
##   72 | 
##   74 | 
##   76 | 1
##   78 | 
##   80 | 
##   82 | 
##   84 | 
##   86 | 
##   88 | 
##   90 | 33
Missing data patterns


Participants with <20% missing data (n=509):

## # A tibble: 45 × 3
##    variable                        n_miss pct_miss
##    <chr>                            <int>    <num>
##  1 Gender_bin                           0    0    
##  2 Age                                  2    0.393
##  3 Retired_bin                          0    0    
##  4 Volunteer                            0    0    
##  5 Lives_alone_bin                      0    0    
##  6 Phys_health_rating                   7    1.38 
##  7 Multimorbidity_score                 0    0    
##  8 Subj_vision_loss_bin                18    3.54 
##  9 Subj_vision_rating_aided             1    0.196
## 10 Subj_hearing_loss_bin               36    7.07 
## 11 any_hearing_device                   0    0    
## 12 study2_HA                            0    0    
## 13 Subj_hearing_rating_aided_REV      159   31.2  
## 14 Subj_hearing_rating_unaided_REV      8    1.57 
## 15 Tinnitus_past_wk_bin                 0    0    
## 16 ssq_speech_REV                      46    9.04 
## 17 ssq_spatial_REV                     51   10.0  
## 18 ssq_qualities_REV                    3    0.589
## 19 SIM_mean                            12    2.36 
## 20 Emocheq_mean                         8    1.57 
## 21 hhies_emo_total                      0    0    
## 22 hhies_soc_total                      0    0    
## 23 positive_SCI_bin                     0    0    
## 24 CSRQ_mean                            0    0    
## 25 Mobility_needs_bin                   0    0    
## 26 ABC_mean                             0    0    
## 27 SWLS_mean                            0    0    
## 28 WHOQOL_overall_qol                   0    0    
## 29 WHOQOL_health_qol                    0    0    
## 30 WHOQOL_Dom1_phys                     0    0    
## 31 WHOQOL_Dom2_psy                      0    0    
## 32 WHOQOL_Dom3_soc                      1    0.196
## 33 WHOQOL_Dom4_env                      0    0    
## 34 WHO_money                            0    0    
## 35 PHQ4_anx_mean                        1    0.196
## 36 PHQ4_dep_mean                        1    0.196
## 37 Lonely_bin                           1    0.196
## 38 Social_network_index                 1    0.196
## 39 Soc_part_freq                        1    0.196
## 40 Soc_part_types                       1    0.196
## 41 Socsupp_mean                         5    0.982
## 42 Connections_total                    9    1.77 
## 43 Motivate_mean                        5    0.982
## 44 study1_HA_bin                       78   15.3  
## 45 PTA4_better_ear                     73   14.3


Participants with >39%% missing data (n=18):


(iv) Justify discarding/retaining participants

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Drop 2 cases that are fully missing
##     Progress Duration.in.seconds Finished
## 458        0                 217        0
## 467        1                 540        0
## # A tibble: 46 × 3
##    variable                        n_miss pct_miss
##    <chr>                            <int>    <num>
##  1 Gender_bin                           2      100
##  2 Age                                  2      100
##  3 Retired_bin                          2      100
##  4 Volunteer                            2      100
##  5 Lives_alone_bin                      2      100
##  6 Phys_health_rating                   2      100
##  7 Multimorbidity_score                 0        0
##  8 Subj_vision_loss_bin                 2      100
##  9 Subj_vision_rating_aided             2      100
## 10 Subj_hearing_loss_bin                2      100
## 11 any_hearing_device                   0        0
## 12 study2_HA                            0        0
## 13 Subj_hearing_rating_aided_REV        2      100
## 14 Subj_hearing_rating_unaided_REV      2      100
## 15 Tinnitus_past_wk_bin                 0        0
## 16 ssq_speech_REV                       2      100
## 17 ssq_spatial_REV                      2      100
## 18 ssq_qualities_REV                    2      100
## 19 SIM_mean                             2      100
## 20 Emocheq_mean                         2      100
## 21 hhies_emo_total                      2      100
## 22 hhies_soc_total                      2      100
## 23 positive_SCI_bin                     2      100
## 24 CSRQ_mean                            2      100
## 25 Mobility_needs_bin                   2      100
## 26 ABC_mean                             2      100
## 27 SWLS_mean                            2      100
## 28 WHOQOL_overall_qol                   2      100
## 29 WHOQOL_health_qol                    2      100
## 30 WHOQOL_Dom1_phys                     2      100
## 31 WHOQOL_Dom2_psy                      2      100
## 32 WHOQOL_Dom3_soc                      2      100
## 33 WHOQOL_Dom4_env                      2      100
## 34 WHO_money                            2      100
## 35 PHQ4_anx_mean                        2      100
## 36 PHQ4_dep_mean                        2      100
## 37 Lonely_bin                           2      100
## 38 Social_network_index                 2      100
## 39 Soc_part_freq                        2      100
## 40 Soc_part_types                       2      100
## 41 Socsupp_mean                         2      100
## 42 Connections_total                    2      100
## 43 Motivate_mean                        2      100
## 44 study1_HA_bin                        2      100
## 45 PTA4_better_ear                      2      100
## 46 PTA4_asym                            2      100
Retain 16 that mostly have age, audiogram, earlier measures
##     Progress Duration.in.seconds Finished
## 45        58                 413        0
## 77        19                 247        0
## 136       58              308782        0
## 153       30                 449        0
## 166       52                 185        0
## 176       53                1693        0
## 187       53              518035        0
## 192       45              504174        0
## 228       13                  96        0
## 246       64                1719        0
## 318       55                 466        0
## 364       55                 988        0
## 405       55                 650        0
## 483       45                 731        0
## 520       64                6724        0
## 522       70                2376        0
## # A tibble: 46 × 3
##    variable                        n_miss pct_miss
##    <chr>                            <int>    <num>
##  1 Gender_bin                           0     0   
##  2 Age                                  1     6.25
##  3 Retired_bin                          0     0   
##  4 Volunteer                            0     0   
##  5 Lives_alone_bin                      0     0   
##  6 Phys_health_rating                   2    12.5 
##  7 Multimorbidity_score                 0     0   
##  8 Subj_vision_loss_bin                 2    12.5 
##  9 Subj_vision_rating_aided             2    12.5 
## 10 Subj_hearing_loss_bin                3    18.8 
## 11 any_hearing_device                   0     0   
## 12 study2_HA                            0     0   
## 13 Subj_hearing_rating_aided_REV        8    50   
## 14 Subj_hearing_rating_unaided_REV      3    18.8 
## 15 Tinnitus_past_wk_bin                 0     0   
## 16 ssq_speech_REV                      13    81.2 
## 17 ssq_spatial_REV                     11    68.8 
## 18 ssq_qualities_REV                    6    37.5 
## 19 SIM_mean                            11    68.8 
## 20 Emocheq_mean                        11    68.8 
## 21 hhies_emo_total                     13    81.2 
## 22 hhies_soc_total                     13    81.2 
## 23 positive_SCI_bin                    13    81.2 
## 24 CSRQ_mean                           15    93.8 
## 25 Mobility_needs_bin                  15    93.8 
## 26 ABC_mean                            15    93.8 
## 27 SWLS_mean                           15    93.8 
## 28 WHOQOL_overall_qol                  16   100   
## 29 WHOQOL_health_qol                   16   100   
## 30 WHOQOL_Dom1_phys                    16   100   
## 31 WHOQOL_Dom2_psy                     16   100   
## 32 WHOQOL_Dom3_soc                     16   100   
## 33 WHOQOL_Dom4_env                     16   100   
## 34 WHO_money                           16   100   
## 35 PHQ4_anx_mean                       16   100   
## 36 PHQ4_dep_mean                       16   100   
## 37 Lonely_bin                          16   100   
## 38 Social_network_index                16   100   
## 39 Soc_part_freq                       16   100   
## 40 Soc_part_types                      16   100   
## 41 Socsupp_mean                        16   100   
## 42 Connections_total                   16   100   
## 43 Motivate_mean                       16   100   
## 44 study1_HA_bin                        3    18.8 
## 45 PTA4_better_ear                      3    18.8 
## 46 PTA4_asym                            3    18.8


(v) Variable relationships

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Correlations heatmap: Hearing

Correlations heatmap: Physical health
PCA

Note: PC1 and PC2 account for 36% of the total variance.



2. Imputation using MICE

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Current method

  • Use predictors that correlate 0.5 or better to impute missing data in a variable (30 variables); if no such predictors, adjust threshold to 0.4 (3 variables), then 0.3, then 0.2 (2 variables)
    pdf
  • Eight variables are complete and do not require imputing; 2 variables have no predictors that correlate at least r = 0.2 (Subj_vision_loss_bin, Connections_total)
  • MICE settings: total of 5 imputed datasets, with a maximum of 10 iterations per dataset, using predictive means matching to impute missing values

Check imputed data

  • Convergence
    pdf

  • Compare imputed to observed data
    pdf

  • Characteristics of imputed data
    pdf

PCA with standardized imputed data

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PCA

Note: This is only 1 of 5 imputed datasets, but the plots are similar.



3. Predicting hearing aid adoption

Complete cases vs. imputed data

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Note: All participants together; not filtered by hearing aid candidacy.

Regression output (complete cases, n=346)

Non-hearing aid users = 267
Hearing aid users = 79 (22.8%)
Note: Dropped Subj_hearing_rating_aided_REV & SWLS_mean due to VIF > 5


##                               Term Estimate StdError       z      p     OddsRatio CIlower CIupper
## 1                      (Intercept) -24.5645 884.2355 -0.0278 0.9778        0.0000  0.0000     Inf
## 2                       Gender_bin   0.5265   0.4564  1.1536 0.2487        1.6930  0.6921  4.1418
## 3                              Age  -0.0185   0.0346 -0.5336 0.5936        0.9817  0.9172  1.0506
## 4                      Retired_bin   0.0571   0.5098  0.1121 0.9108        1.0588  0.3898  2.8757
## 5                    Volunteer_rec   0.5477   0.2816  1.9448 0.0518        1.7293  0.9957  3.0031
## 6                  Lives_alone_bin  -0.2751   0.5566 -0.4943 0.6211        0.7595  0.2551  2.2608
## 7               Phys_health_rating   0.0966   0.3728  0.2590 0.7956        1.1014  0.5304  2.2868
## 8             Multimorbidity_score  -0.0199   0.1206 -0.1652 0.8688        0.9803  0.7739  1.2417
## 9               Mobility_needs_bin  -0.3204   1.1148 -0.2874 0.7738        0.7258  0.0816  6.4536
## 10                        ABC_mean  -0.0315   0.0261 -1.2055 0.2280        0.9690  0.9206  1.0199
## 11        Subj_vision_rating_aided   0.0508   0.2960  0.1717 0.8637        1.0521  0.5890  1.8795
## 12           Subj_hearing_loss_bin  17.0709 884.2210  0.0193 0.9846 25929967.6016  0.0000     Inf
## 13 Subj_hearing_rating_unaided_REV   1.0591   0.3850  2.7506 0.0059        2.8837  1.3559  6.1334
## 14            Tinnitus_past_wk_bin   0.1555   0.4104  0.3790 0.7047        1.1683  0.5227  2.6112
## 15                 PTA4_better_ear   0.1214   0.0288  4.2225 0.0000        1.1291  1.0672  1.1945
## 16                       PTA4_asym   0.0472   0.0153  3.0891 0.0020        1.0483  1.0174  1.0802
## 17                 SSQ15i_mean_REV  -0.6680   0.1855 -3.6002 0.0003        0.5128  0.3564  0.7376
## 18                    Emocheq_mean  -0.0308   0.2780 -0.1108 0.9118        0.9697  0.5623  1.6721
## 19                     HHIES_total   0.0596   0.0386  1.5445 0.1225        1.0614  0.9841  1.1448
## 20                        SIM_mean  -0.1358   0.1165 -1.1662 0.2435        0.8730  0.6948  1.0968
## 21                positive_SCI_bin   1.1976   0.7118  1.6824 0.0925        3.3122  0.8207 13.3674
## 22                       CSRQ_mean  -0.1344   0.6195 -0.2170 0.8282        0.8742  0.2596  2.9440
## 23                   PHQ4_anx_mean   1.5003   0.4999  3.0009 0.0027        4.4829  1.6827 11.9431
## 24                   PHQ4_dep_mean  -1.1449   0.6681 -1.7137 0.0866        0.3183  0.0859  1.1788
## 25              WHOQOL_overall_qol  -0.4355   0.4717 -0.9233 0.3558        0.6469  0.2567  1.6306
## 26               WHOQOL_health_qol   0.3760   0.3228  1.1648 0.2441        1.4565  0.7736  2.7421
## 27                       WHO_money   0.8039   0.2691  2.9869 0.0028        2.2343  1.3184  3.7865
## 28                    Socsupp_mean   0.2161   0.2994  0.7216 0.4705        1.2412  0.6902  2.2320
## 29            Social_network_index  -0.1362   0.1756 -0.7754 0.4381        0.8727  0.6185  1.2313
## 30                   Soc_part_freq  -0.2681   0.3671 -0.7303 0.4652        0.7648  0.3724  1.5706
## 31                  Soc_part_types   0.0183   0.1582  0.1155 0.9080        1.0184  0.7469  1.3886
## 32                      Lonely_bin  -0.2511   0.6864 -0.3658 0.7145        0.7780  0.2026  2.9868
## 33                   Motivate_mean   0.3051   0.2395  1.2743 0.2026        1.3568  0.8486  2.1694
Regression output (imputed data, n=525)
##                               Term Estimate StdError       t       df      p OddsRatio CIlower CIupper
## 1                      (Intercept)  -0.6315   0.3524 -1.7921 276.6114 0.0742    0.5318  0.2665  1.0610
## 2                       Gender_bin   0.0568   0.0364  1.5602 464.2247 0.1194    1.0584  0.9856  1.1367
## 3                              Age   0.0025   0.0025  0.9939 368.6422 0.3209    1.0025  0.9976  1.0074
## 4                      Retired_bin  -0.0288   0.0369 -0.7805 489.2480 0.4355    0.9716  0.9038  1.0445
## 5                    Volunteer_rec   0.0441   0.0206  2.1351 465.5042 0.0333    1.0451  1.0037  1.0881
## 6                  Lives_alone_bin  -0.0227   0.0422 -0.5367 441.5722 0.5918    0.9776  0.9000  1.0618
## 7               Phys_health_rating  -0.0024   0.0276 -0.0876 255.2605 0.9303    0.9976  0.9451  1.0531
## 8             Multimorbidity_score   0.0044   0.0077  0.5713 485.2053 0.5680    1.0044  0.9894  1.0197
## 9               Mobility_needs_bin  -0.0268   0.0880 -0.3049 209.2891 0.7607    0.9736  0.8193  1.1568
## 10                        ABC_mean  -0.0032   0.0017 -1.9151 340.0681 0.0563    0.9968  0.9935  1.0001
## 11        Subj_vision_rating_aided   0.0102   0.0234  0.4366 461.3953 0.6626    1.0103  0.9650  1.0577
## 12           Subj_hearing_loss_bin   0.0967   0.0509  1.8974 250.9344 0.0589    1.1015  0.9969  1.2171
## 13 Subj_hearing_rating_unaided_REV   0.0969   0.0253  3.8330 470.9501 0.0001    1.1018  1.0484  1.1578
## 14            Tinnitus_past_wk_bin  -0.0540   0.0348 -1.5504 478.5980 0.1217    0.9474  0.8850  1.0143
## 15                 PTA4_better_ear   0.0077   0.0023  3.3060  67.9205 0.0015    1.0077  1.0032  1.0123
## 16                       PTA4_asym   0.0028   0.0015  1.8414  96.0029 0.0686    1.0028  0.9999  1.0058
## 17                 SSQ15i_mean_REV  -0.0681   0.0134 -5.0894 450.3870 0.0000    0.9342  0.9100  0.9590
## 18                    Emocheq_mean  -0.0051   0.0218 -0.2358 305.8811 0.8137    0.9949  0.9533  1.0383
## 19                     HHIES_total   0.0063   0.0031  2.0697 133.4496 0.0404    1.0063  1.0002  1.0125
## 20                        SIM_mean  -0.0037   0.0086 -0.4279 151.9795 0.6693    0.9963  0.9797  1.0132
## 21                positive_SCI_bin   0.0445   0.0596  0.7467 242.5054 0.4560    1.0455  0.9302  1.1751
## 22                       CSRQ_mean  -0.0476   0.0499 -0.9535 295.2604 0.3411    0.9535  0.8647  1.0515
## 23                   PHQ4_anx_mean   0.1187   0.0375  3.1691 394.3012 0.0016    1.1260  1.0462  1.2119
## 24                   PHQ4_dep_mean  -0.0099   0.0438 -0.2265 396.3896 0.8209    0.9901  0.9087  1.0789
## 25              WHOQOL_overall_qol   0.0216   0.0339  0.6378 371.0423 0.5240    1.0218  0.9561  1.0920
## 26               WHOQOL_health_qol   0.0262   0.0241  1.0900 212.9481 0.2769    1.0265  0.9792  1.0762
## 27                       WHO_money   0.0327   0.0190  1.7210 394.3536 0.0860    1.0332  0.9955  1.0724
## 28                    Socsupp_mean   0.0126   0.0244  0.5183 211.7117 0.6048    1.0127  0.9654  1.0623
## 29            Social_network_index  -0.0052   0.0142 -0.3641 302.9319 0.7160    0.9948  0.9675  1.0229
## 30                   Soc_part_freq   0.0043   0.0280  0.1529 363.5837 0.8786    1.0043  0.9507  1.0610
## 31                  Soc_part_types  -0.0056   0.0129 -0.4309 350.2229 0.6668    0.9944  0.9696  1.0199
## 32                      Lonely_bin  -0.0041   0.0492 -0.0834 235.7455 0.9336    0.9959  0.9044  1.0967
## 33                   Motivate_mean   0.0172   0.0208  0.8282 205.3380 0.4085    1.0173  0.9767  1.0597


Legend: Asterisks denote p < 0.05; crosses denote p [0.05, 0.1]


Accuracy of model predictions

Note: Not really a fair comparison as models and model coefficients are different between complete-cases and imputed data.

## [1] "Complete cases, using median as boundary"
##       predicted
## actual   0   1
##      0 170  97
##      1   3  76
## [1] "Accuracy: 0.711"
## [1] "Sensitivity: 0.962"
## [1] "Specificity: 0.637"

## [1] "Imputed data, using median as boundary"
##       predicted
## actual   0   1
##      0 256 166
##      1   7  96
## [1] "Accuracy: 0.67"
## [1] "Sensitivity: 0.932"
## [1] "Specificity: 0.607"


Grouping by HHIE-S status

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Counts

0-8 no handicap, 10-24 mild to moderate, 26-40 severe

##       HHIES
## UseHA  None MildMod Sev <NA>
##   0     233     148  30   11
##   1      26      62  13    2
##   <NA>    0       0   0    0
## [1] 0.100 0.295 0.302 0.154
Regression output (imputed data, n=525)
##                               Term Estimate StdError       t       df      p OddsRatio CIlower CIupper
## 1                      (Intercept)   0.1820   0.4579  0.3975 184.9446 0.6915    1.1996  0.4890  2.9432
## 2                       Gender_bin  -0.0324   0.0425 -0.7629 223.0138 0.4463    0.9681  0.8907  1.0522
## 3                              Age  -0.0003   0.0030 -0.0901 195.9660 0.9283    0.9997  0.9938  1.0056
## 4                      Retired_bin  -0.0199   0.0414 -0.4796 220.4080 0.6320    0.9803  0.9039  1.0632
## 5                    Volunteer_rec   0.0330   0.0231  1.4277 220.1416 0.1548    1.0336  0.9878  1.0814
## 6                  Lives_alone_bin   0.0398   0.0462  0.8619 220.8280 0.3897    1.0406  0.9505  1.1392
## 7               Phys_health_rating  -0.0295   0.0316 -0.9338 215.7385 0.3514    0.9709  0.9126  1.0330
## 8             Multimorbidity_score   0.0100   0.0112  0.8994 221.5558 0.3694    1.0101  0.9881  1.0325
## 9               Mobility_needs_bin   0.0200   0.1146  0.1743 214.5812 0.8618    1.0202  0.8150  1.2771
## 10                        ABC_mean  -0.0013   0.0026 -0.5150 222.9350 0.6070    0.9987  0.9936  1.0038
## 11        Subj_vision_rating_aided  -0.0232   0.0283 -0.8191 217.9952 0.4137    0.9771  0.9243  1.0328
## 12           Subj_hearing_loss_bin   0.0907   0.0500  1.8134 221.0009 0.0711    1.0949  0.9927  1.2077
## 13 Subj_hearing_rating_unaided_REV   0.0480   0.0293  1.6373 201.5816 0.1031    1.0492  0.9906  1.1112
## 14            Tinnitus_past_wk_bin  -0.0518   0.0426 -1.2149 221.3570 0.2257    0.9495  0.8735  1.0322
## 15                 PTA4_better_ear   0.0096   0.0029  3.3417 105.3083 0.0012    1.0096  1.0039  1.0154
## 16                       PTA4_asym   0.0043   0.0033  1.2809  29.0812 0.2103    1.0043  0.9978  1.0108
## 17                 SSQ15i_mean_REV  -0.0507   0.0202 -2.5085 136.4313 0.0133    0.9506  0.9137  0.9890
## 18                    Emocheq_mean  -0.0075   0.0287 -0.2608 220.4529 0.7945    0.9925  0.9382  1.0500
## 19                     HHIES_total   0.0042   0.0075  0.5599 219.0492 0.5761    1.0042  0.9896  1.0191
## 20                        SIM_mean   0.0027   0.0094  0.2829 203.4663 0.7775    1.0027  0.9844  1.0213
## 21                positive_SCI_bin   0.1467   0.1061  1.3818 179.8757 0.1687    1.1580  0.9406  1.4257
## 22                       CSRQ_mean  -0.0401   0.0542 -0.7408 220.0583 0.4596    0.9607  0.8639  1.0684
## 23                   PHQ4_anx_mean   0.1012   0.0464  2.1797 215.6318 0.0304    1.1065  1.0103  1.2118
## 24                   PHQ4_dep_mean  -0.0816   0.0620 -1.3160 190.8040 0.1897    0.9216  0.8162  1.0407
## 25              WHOQOL_overall_qol  -0.0135   0.0396 -0.3400 169.8827 0.7342    0.9866  0.9129  1.0662
## 26               WHOQOL_health_qol   0.0028   0.0274  0.1017 202.2451 0.9191    1.0028  0.9504  1.0581
## 27                       WHO_money   0.0439   0.0236  1.8575 222.3239 0.0646    1.0449  0.9976  1.0943
## 28                    Socsupp_mean   0.0169   0.0288  0.5847 215.6693 0.5593    1.0170  0.9612  1.0761
## 29            Social_network_index  -0.0099   0.0154 -0.6442 221.9440 0.5201    0.9901  0.9607  1.0205
## 30                   Soc_part_freq  -0.0144   0.0339 -0.4240 196.2709 0.6720    0.9857  0.9223  1.0534
## 31                  Soc_part_types  -0.0068   0.0141 -0.4820 211.5570 0.6303    0.9932  0.9662  1.0211
## 32                      Lonely_bin  -0.0188   0.0621 -0.3029 215.1029 0.7623    0.9814  0.8689  1.1084
## 33                   Motivate_mean  -0.0219   0.0236 -0.9263 218.2957 0.3553    0.9783  0.9341  1.0247
##                               Term Estimate StdError       t       df      p OddsRatio CIlower CIupper
## 1                      (Intercept)  -1.3437   0.5910 -2.2736 120.1590 0.0248    0.2609  0.0819  0.8308
## 2                       Gender_bin   0.1154   0.0656  1.7610 190.7221 0.0798    1.1223  0.9869  1.2763
## 3                              Age   0.0055   0.0045  1.2130 125.6280 0.2274    1.0055  0.9967  1.0144
## 4                      Retired_bin  -0.0555   0.0660 -0.8412 216.1656 0.4012    0.9460  0.8312  1.0767
## 5                    Volunteer_rec   0.0432   0.0373  1.1577 214.4456 0.2483    1.0441  0.9705  1.1233
## 6                  Lives_alone_bin  -0.1331   0.0771 -1.7270 214.9260 0.0856    0.8754  0.7526  1.0182
## 7               Phys_health_rating   0.0198   0.0460  0.4290 210.7546 0.6684    1.0200  0.9321  1.1162
## 8             Multimorbidity_score   0.0002   0.0114  0.0177 207.7522 0.9859    1.0002  0.9781  1.0228
## 9               Mobility_needs_bin  -0.0133   0.1355 -0.0983 110.1941 0.9219    0.9868  0.7566  1.2870
## 10                        ABC_mean  -0.0046   0.0023 -1.9778 199.9140 0.0493    0.9954  0.9909  0.9999
## 11        Subj_vision_rating_aided   0.0365   0.0383  0.9537 209.6346 0.3413    1.0372  0.9622  1.1180
## 12           Subj_hearing_loss_bin   0.0962   0.1114  0.8629 156.6792 0.3895    1.1010  0.8850  1.3696
## 13 Subj_hearing_rating_unaided_REV   0.1392   0.0458  3.0388 201.9831 0.0027    1.1494  1.0507  1.2573
## 14            Tinnitus_past_wk_bin  -0.0378   0.0561 -0.6736 204.9458 0.5013    0.9629  0.8626  1.0748
## 15                 PTA4_better_ear   0.0087   0.0040  2.2070  27.3523 0.0359    1.0087  1.0009  1.0167
## 16                       PTA4_asym   0.0027   0.0022  1.2042  33.3114 0.2370    1.0027  0.9984  1.0070
## 17                 SSQ15i_mean_REV  -0.0731   0.0198 -3.6932 209.1921 0.0003    0.9295  0.8941  0.9663
## 18                    Emocheq_mean   0.0079   0.0330  0.2390 213.6771 0.8113    1.0079  0.9448  1.0753
## 19                     HHIES_total   0.0035   0.0054  0.6545 151.9871 0.5138    1.0035  0.9929  1.0142
## 20                        SIM_mean  -0.0196   0.0140 -1.4050 206.7695 0.1615    0.9806  0.9540  1.0079
## 21                positive_SCI_bin   0.0849   0.0837  1.0151 208.2619 0.3112    1.0886  0.9239  1.2827
## 22                       CSRQ_mean  -0.0362   0.0969 -0.3735  85.0238 0.7097    0.9644  0.7976  1.1662
## 23                   PHQ4_anx_mean   0.0908   0.0631  1.4380 174.8102 0.1522    1.0950  0.9677  1.2392
## 24                   PHQ4_dep_mean   0.0477   0.0661  0.7216 195.9784 0.4714    1.0489  0.9214  1.1939
## 25              WHOQOL_overall_qol   0.0637   0.0623  1.0229 117.2228 0.3085    1.0658  0.9433  1.2042
## 26               WHOQOL_health_qol   0.0395   0.0406  0.9742 206.4644 0.3311    1.0403  0.9607  1.1265
## 27                       WHO_money   0.0224   0.0320  0.6982 108.0940 0.4866    1.0227  0.9605  1.0888
## 28                    Socsupp_mean  -0.0181   0.0401 -0.4508 175.4000 0.6527    0.9821  0.9078  1.0624
## 29            Social_network_index   0.0009   0.0244  0.0354 213.3367 0.9718    1.0009  0.9542  1.0499
## 30                   Soc_part_freq   0.0237   0.0471  0.5032 141.1688 0.6156    1.0240  0.9337  1.1230
## 31                  Soc_part_types  -0.0044   0.0232 -0.1909 215.6324 0.8488    0.9956  0.9514  1.0419
## 32                      Lonely_bin   0.0206   0.0787  0.2614 207.1554 0.7941    1.0208  0.8749  1.1911
## 33                   Motivate_mean   0.0714   0.0364  1.9596 170.0572 0.0517    1.0740  1.0001  1.1534


Legend: Asterisks denote p < 0.05; crosses denote p [0.05, 0.1]


Grouping by vision status

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Counts
## 
##    0    1 <NA> 
##  215  290   20
Regression output (imputed data, n=525)
##                               Term Estimate StdError       t       df      p OddsRatio CIlower CIupper
## 1                      (Intercept)  -0.2397   0.5665 -0.4232 177.5691 0.6727    0.7869  0.2592  2.3884
## 2                       Gender_bin   0.0265   0.0509  0.5211 175.9306 0.6030    1.0269  0.9294  1.1346
## 3                              Age  -0.0015   0.0040 -0.3873 136.0409 0.6991    0.9985  0.9907  1.0064
## 4                      Retired_bin  -0.0387   0.0539 -0.7179 178.6501 0.4738    0.9620  0.8656  1.0692
## 5                    Volunteer_rec   0.0674   0.0295  2.2825 172.6445 0.0237    1.0697  1.0096  1.1334
## 6                  Lives_alone_bin  -0.1206   0.0628 -1.9226 177.3012 0.0561    0.8864  0.7837  1.0025
## 7               Phys_health_rating  -0.0331   0.0401 -0.8259 176.2923 0.4100    0.9674  0.8943  1.0465
## 8             Multimorbidity_score   0.0165   0.0139  1.1875 179.6094 0.2366    1.0166  0.9893  1.0447
## 9               Mobility_needs_bin  -0.0902   0.1324 -0.6811 178.8297 0.4967    0.9137  0.7049  1.1845
## 10                        ABC_mean  -0.0048   0.0033 -1.4298 178.5234 0.1545    0.9952  0.9888  1.0017
## 11        Subj_vision_rating_aided   0.0063   0.0366  0.1724 177.8264 0.8633    1.0063  0.9367  1.0812
## 12           Subj_hearing_loss_bin   0.0970   0.0747  1.2994 105.9267 0.1966    1.1019  0.9518  1.2756
## 13 Subj_hearing_rating_unaided_REV   0.0246   0.0382  0.6426 172.8972 0.5213    1.0249  0.9510  1.1046
## 14            Tinnitus_past_wk_bin  -0.0344   0.0560 -0.6151 150.4324 0.5394    0.9662  0.8657  1.0783
## 15                 PTA4_better_ear   0.0096   0.0039  2.4327  19.2745 0.0249    1.0096  1.0020  1.0174
## 16                       PTA4_asym   0.0037   0.0021  1.8059 175.6367 0.0726    1.0037  0.9996  1.0078
## 17                 SSQ15i_mean_REV  -0.0513   0.0212 -2.4239 179.0321 0.0164    0.9500  0.9113  0.9903
## 18                    Emocheq_mean   0.0016   0.0337  0.0464 151.5597 0.9630    1.0016  0.9376  1.0700
## 19                     HHIES_total   0.0091   0.0046  1.9594 160.5738 0.0518    1.0091  1.0001  1.0183
## 20                        SIM_mean   0.0041   0.0116  0.3558 176.2630 0.7224    1.0041  0.9815  1.0272
## 21                positive_SCI_bin  -0.0882   0.0982 -0.8979 157.8400 0.3706    0.9156  0.7553  1.1099
## 22                       CSRQ_mean  -0.0516   0.0738 -0.6988 141.7428 0.4858    0.9497  0.8218  1.0975
## 23                   PHQ4_anx_mean   0.1025   0.0546  1.8754 178.4944 0.0624    1.1079  0.9955  1.2331
## 24                   PHQ4_dep_mean  -0.0202   0.0721 -0.2800 167.4595 0.7798    0.9800  0.8509  1.1288
## 25              WHOQOL_overall_qol   0.0138   0.0508  0.2723 179.3228 0.7857    1.0139  0.9178  1.1200
## 26               WHOQOL_health_qol   0.0634   0.0353  1.7956 173.3409 0.0743    1.0655  0.9942  1.1418
## 27                       WHO_money   0.0270   0.0272  0.9937 176.1375 0.3217    1.0274  0.9740  1.0836
## 28                    Socsupp_mean   0.0287   0.0343  0.8354 155.9077 0.4048    1.0291  0.9622  1.1007
## 29            Social_network_index   0.0006   0.0197  0.0321 179.6335 0.9744    1.0006  0.9627  1.0400
## 30                   Soc_part_freq   0.0706   0.0433  1.6318 165.8645 0.1046    1.0732  0.9858  1.1682
## 31                  Soc_part_types  -0.0157   0.0192 -0.8163 170.5264 0.4154    0.9844  0.9481  1.0222
## 32                      Lonely_bin  -0.0049   0.0748 -0.0659 153.1799 0.9476    0.9951  0.8594  1.1522
## 33                   Motivate_mean  -0.0062   0.0291 -0.2129 179.4084 0.8317    0.9938  0.9387  1.0522
##                               Term Estimate StdError       t       df      p OddsRatio CIlower CIupper
## 1                      (Intercept)  -1.3177   0.4871 -2.7050 136.8350 0.0077    0.2678  0.1031  0.6956
## 2                       Gender_bin   0.1145   0.0559  2.0474 180.1686 0.0421    1.1213  1.0049  1.2512
## 3                              Age   0.0067   0.0036  1.8534 236.6930 0.0651    1.0067  0.9996  1.0139
## 4                      Retired_bin  -0.0487   0.0518 -0.9402 250.3118 0.3480    0.9525  0.8605  1.0542
## 5                    Volunteer_rec   0.0399   0.0309  1.2922 189.7278 0.1979    1.0407  0.9795  1.1057
## 6                  Lives_alone_bin   0.0749   0.0612  1.2239 197.1641 0.2224    1.0778  0.9559  1.2151
## 7               Phys_health_rating   0.0277   0.0384  0.7212 133.2852 0.4720    1.0281  0.9535  1.1085
## 8             Multimorbidity_score  -0.0054   0.0097 -0.5537 253.4107 0.5803    0.9946  0.9759  1.0137
## 9               Mobility_needs_bin   0.0269   0.1208  0.2223 122.7111 0.8244    1.0273  0.8107  1.3017
## 10                        ABC_mean  -0.0021   0.0021 -1.0411 161.2161 0.2994    0.9979  0.9938  1.0020
## 11        Subj_vision_rating_aided   0.0013   0.0327  0.0396 243.8964 0.9684    1.0013  0.9391  1.0676
## 12           Subj_hearing_loss_bin   0.0738   0.0715  1.0317 183.3870 0.3036    1.0766  0.9358  1.2385
## 13 Subj_hearing_rating_unaided_REV   0.1160   0.0348  3.3312 251.9835 0.0010    1.1230  1.0490  1.2023
## 14            Tinnitus_past_wk_bin  -0.0471   0.0474 -0.9933 251.3714 0.3215    0.9540  0.8694  1.0469
## 15                 PTA4_better_ear   0.0066   0.0031  2.1470  93.4544 0.0344    1.0066  1.0005  1.0128
## 16                       PTA4_asym   0.0017   0.0021  0.8181 107.9354 0.4151    1.0017  0.9976  1.0058
## 17                 SSQ15i_mean_REV  -0.1001   0.0186 -5.3834 184.6014 0.0000    0.9047  0.8724  0.9383
## 18                    Emocheq_mean  -0.0072   0.0294 -0.2458 155.3778 0.8062    0.9928  0.9372  1.0517
## 19                     HHIES_total   0.0091   0.0040  2.2698 118.3115 0.0250    1.0091  1.0013  1.0171
## 20                        SIM_mean  -0.0117   0.0116 -1.0042 181.9076 0.3166    0.9884  0.9662  1.0111
## 21                positive_SCI_bin   0.0929   0.0772  1.2026 167.4327 0.2308    1.0974  0.9433  1.2766
## 22                       CSRQ_mean   0.0415   0.0727  0.5710 121.2021 0.5690    1.0424  0.9039  1.2020
## 23                   PHQ4_anx_mean   0.1570   0.0523  3.0022 213.0446 0.0030    1.1700  1.0560  1.2963
## 24                   PHQ4_dep_mean  -0.0272   0.0580 -0.4683 209.2524 0.6401    0.9732  0.8686  1.0903
## 25              WHOQOL_overall_qol   0.0870   0.0487  1.7857 193.4626 0.0757    1.0909  0.9916  1.2002
## 26               WHOQOL_health_qol   0.0138   0.0331  0.4177 143.5408 0.6768    1.0139  0.9502  1.0819
## 27                       WHO_money   0.0240   0.0274  0.8746 175.2817 0.3830    1.0243  0.9707  1.0808
## 28                    Socsupp_mean  -0.0012   0.0411 -0.0286  41.6853 0.9773    0.9988  0.9215  1.0826
## 29            Social_network_index   0.0003   0.0210  0.0131 145.0681 0.9896    1.0003  0.9600  1.0423
## 30                   Soc_part_freq  -0.0415   0.0403 -1.0298 151.6512 0.3047    0.9593  0.8865  1.0382
## 31                  Soc_part_types   0.0010   0.0188  0.0556 149.3415 0.9557    1.0010  0.9648  1.0386
## 32                      Lonely_bin  -0.0341   0.0688 -0.4954 158.2663 0.6210    0.9665  0.8446  1.1060
## 33                   Motivate_mean   0.0204   0.0308  0.6642  79.5828 0.5085    1.0206  0.9608  1.0841


Legend: Asterisks denote p < 0.05; crosses denote p [0.05, 0.1]


Variable selection: Predicting HA adoption

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Penalized logistic regression (LASSO) with 5-fold cross-validation was conducted across 100 lambda (penalty) values. The lambda value that led to the best-fitting model (with lowest cross-validation error) was 0.044, which corresponds to a model with 13 predictors:

Regression output (13 selected) (imputed data, n=525)
##                               Term Estimate StdError       t       df      p OddsRatio CIlower CIupper
## 1                      (Intercept)  -0.7963   0.1793 -4.4423 466.5515 0.0000    0.4510  0.3174  0.6409
## 2                       Gender_bin   0.0355   0.0325  1.0917 489.3016 0.2755    1.0361  0.9722  1.1043
## 3                              Age   0.0022   0.0022  1.0205 290.7249 0.3083    1.0022  0.9979  1.0065
## 4                    Volunteer_rec   0.0421   0.0182  2.3067 472.5371 0.0215    1.0430  1.0064  1.0809
## 5                  Lives_alone_bin  -0.0225   0.0390 -0.5760 497.0567 0.5649    0.9778  0.9058  1.0554
## 6            Subj_hearing_loss_bin   0.0784   0.0482  1.6269 292.9549 0.1048    1.0816  0.9841  1.1887
## 7  Subj_hearing_rating_unaided_REV   0.0945   0.0244  3.8755 431.6994 0.0001    1.0991  1.0478  1.1530
## 8                  PTA4_better_ear   0.0083   0.0023  3.6810  67.2129 0.0005    1.0083  1.0038  1.0129
## 9                        PTA4_asym   0.0031   0.0014  2.1174 138.5066 0.0360    1.0031  1.0004  1.0059
## 10                 SSQ15i_mean_REV  -0.0749   0.0123 -6.0967 272.3709 0.0000    0.9278  0.9057  0.9505
## 11                     HHIES_total   0.0054   0.0025  2.1303 169.9426 0.0346    1.0054  1.0005  1.0104
## 12                   PHQ4_anx_mean   0.0959   0.0293  3.2757 187.7804 0.0013    1.1006  1.0392  1.1657
## 13                       WHO_money   0.0381   0.0178  2.1395 215.4898 0.0335    1.0388  1.0032  1.0757
## 14                    Socsupp_mean   0.0268   0.0208  1.2879 333.0934 0.1987    1.0272  0.9861  1.0699


Limiting the model to the 8 predictors with p < 0.05, all 8 predictors remain significant in a standard logistic regression model.

Regression output (8 selected) (imputed data, n=525)
##                              Term Estimate StdError       t       df      p OddsRatio CIlower CIupper
## 1                     (Intercept)  -0.6127   0.1044 -5.8707 218.5124 0.0000    0.5419  0.4416  0.6649
## 2                   Volunteer_rec   0.0421   0.0181  2.3210 428.5667 0.0208    1.0430  1.0066  1.0807
## 3 Subj_hearing_rating_unaided_REV   0.1115   0.0225  4.9617 379.4792 0.0000    1.1180  1.0697  1.1684
## 4                 PTA4_better_ear   0.0104   0.0018  5.6517 192.1114 0.0000    1.0105  1.0069  1.0140
## 5                       PTA4_asym   0.0034   0.0014  2.4128 206.3060 0.0167    1.0034  1.0007  1.0062
## 6                 SSQ15i_mean_REV  -0.0755   0.0123 -6.1393 279.6360 0.0000    0.9273  0.9052  0.9499
## 7                     HHIES_total   0.0054   0.0025  2.1268 130.9653 0.0353    1.0054  1.0005  1.0104
## 8                   PHQ4_anx_mean   0.0836   0.0291  2.8772 157.7745 0.0046    1.0872  1.0269  1.1510
## 9                       WHO_money   0.0509   0.0170  2.9949 226.0709 0.0031    1.0522  1.0177  1.0879



Accuracy of model predictions

## [1] "Imputed data, 8 predictors, using median as boundary to classify 0 or 1"
##       predicted
## actual   0   1
##      0 252 170
##      1  11  92
## [1] "Accuracy: 0.655"
## [1] "Sensitivity: 0.893"
## [1] "Specificity: 0.597"


ROC: BPTA4 and HA adoption

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Complete cases only (n=449)
Imputed data (n=525)
##   m best_threshold sensitivity specificity       auc
## 1 1         26.875   0.7087379   0.7654028 0.7811278
## 2 2         26.875   0.6796117   0.7464455 0.7694980
## 3 3         26.875   0.6796117   0.7630332 0.7762849
## 4 4         26.875   0.6990291   0.7677725 0.7731445
## 5 5         25.625   0.7087379   0.7085308 0.7640800


ROC: HHIES and HA adoption

Complete cases only (n=512)
Imputed data (n=525)
##   m best_threshold sensitivity specificity       auc
## 1 1              9   0.7475728    0.563981 0.6803249
## 2 2              9   0.7378641    0.563981 0.6737680
## 3 3              9   0.7378641   0.5687204 0.6774375
## 4 4              9   0.7475728   0.5687204 0.6821539
## 5 5              9   0.7378641    0.563981 0.6734574


ROC: SSQ-15i and HA adoption

Complete cases only (n=455)
Imputed data (n=525)
##   m best_threshold sensitivity specificity       auc
## 1 1       2.156667   0.6893204   0.3838863 0.5199351
## 2 2       2.156667   0.6990291   0.3767773 0.5222128
## 3 3       1.886667    0.631068   0.4336493 0.5233516
## 4 4       2.156667   0.6893204   0.3815166 0.5196475
## 5 5       2.156667   0.7087379   0.3838863 0.5267450


4. Special populations

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The standard relationship, HA ~ BPTA4

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Plots showing thresholds for BPTA4, Asymmetry, HHIES


  • Of the three, BPTA4 is the best standalone predictor of HA adoption.
  • Legend: Red = HA adopters. Lines are thresholds for highest area-under-curve. Complete cases only, n=423.

Comparing three predictors: BPTA4, Asymmetry, HHIES


  • On their own, BPTA4 and HHIES help predict HA adoption. On its own, PTA4 asymmetry doesn’t.
  • When BPTA4 is the main predictor, adding HHIES doesn’t help predict HA adoption, while adding PTA4 asymmetry does help a little.
## Analysis of Deviance Table
## 
## Model 1: study2_HA ~ 1
## Model 2: study2_HA ~ BPTA4
##   Resid. Df Resid. Dev Df Deviance  Pr(>Chi)    
## 1       422     413.17                          
## 2       421     336.89  1   76.272 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Analysis of Deviance Table
## 
## Model 1: study2_HA ~ 1
## Model 2: study2_HA ~ PTA4_asym
##   Resid. Df Resid. Dev Df Deviance Pr(>Chi)  
## 1       422     413.17                       
## 2       421     409.65  1   3.5179  0.06071 .
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Analysis of Deviance Table
## 
## Model 1: study2_HA ~ 1
## Model 2: study2_HA ~ HHIES_total
##   Resid. Df Resid. Dev Df Deviance    Pr(>Chi)    
## 1       422     413.17                            
## 2       421     392.72  1   20.448 0.000006129 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Analysis of Deviance Table
## 
## Model 1: study2_HA ~ BPTA4
## Model 2: study2_HA ~ BPTA4 + PTA4_asym
##   Resid. Df Resid. Dev Df Deviance Pr(>Chi)  
## 1       421     336.89                       
## 2       420     331.60  1   5.2977  0.02135 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Call:
## glm(formula = study2_HA ~ BPTA4 + PTA4_asym, family = "binomial", 
##     data = compdata)
## 
## Coefficients:
##              Estimate Std. Error z value           Pr(>|z|)    
## (Intercept) -4.617386   0.470057  -9.823            < 2e-16 ***
## BPTA4        0.119007   0.015530   7.663 0.0000000000000182 ***
## PTA4_asym    0.022451   0.009219   2.435             0.0149 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 413.17  on 422  degrees of freedom
## Residual deviance: 331.60  on 420  degrees of freedom
## AIC: 337.6
## 
## Number of Fisher Scoring iterations: 5
## Analysis of Deviance Table
## 
## Model 1: study2_HA ~ BPTA4
## Model 2: study2_HA ~ BPTA4 + HHIES_total
##   Resid. Df Resid. Dev Df Deviance Pr(>Chi)  
## 1       421     336.89                       
## 2       420     333.79  1   3.1032  0.07814 .
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Call:
## glm(formula = study2_HA ~ BPTA4 + HHIES_total, family = "binomial", 
##     data = compdata)
## 
## Coefficients:
##             Estimate Std. Error z value         Pr(>|z|)    
## (Intercept) -4.52791    0.46182  -9.804          < 2e-16 ***
## BPTA4        0.10849    0.01569   6.915 0.00000000000469 ***
## HHIES_total  0.02771    0.01568   1.768           0.0771 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 413.17  on 422  degrees of freedom
## Residual deviance: 333.79  on 420  degrees of freedom
## AIC: 339.79
## 
## Number of Fisher Scoring iterations: 5


“Red flag” variables

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Using BPTA4 as the standalone predictor of HA adoption, the sample can be divided into four groups:

##          predicted HA
## actual HA   0   1
##         0 280  85
##         1  23  61


The plot below shows potential “red flag” variables, and which individual participants have them within each group.

Continuous and ordinal variables have been dichotomized according to these cut-offs:
* PTA4 asymmetry ≥ 20 dB HL
* HHIES ≥ 10
* PHQ4 subscores ≥ 3
* Generally, any WHOQOL-BREF responses that are in the worst 2 of 5 categories. There are a few exceptions, where it’s clear that the worst 3 categories are red flags according to the distribution (physical pain, medical treatment, money, information, getting around, health services, transport, negative mood).


Percentages of participants experiencing each “red flag” (same data as above, in table form):

Variable HA_exp_p nonHA_unexp_p nonHA_exp_p HA_unexp_p
1 Asymmetry_bin 3.3 5.9 2.9 17.4
2 HHIES_bin 68.9 54.1 33.9 69.6
3 Tinnitus_past_wk_bin 24.6 41.2 29.3 43.5
4 Mobility_needs_bin 8.2 4.7 5.0 4.3
5 Poor_aided_vision_bin 4.9 1.2 2.9 0.0
6 positive_SCI_bin 11.5 12.9 8.9 17.4
7 PHQ4_anx_bin 42.6 27.1 35.7 47.8
8 PHQ4_dep_bin 18.0 27.1 26.4 30.4
9 Lonely_bin 14.8 22.4 18.6 30.4
10 WHO_qol_bin 6.6 4.7 1.8 0.0
11 WHO_health_satisf_bin 11.5 18.8 11.4 17.4
12 WHO_phys_pain_bin 14.8 24.7 20.4 21.7
13 WHO_med_treatment_bin 13.1 21.2 18.2 8.7
14 WHO_enjoy_life_bin 1.6 5.9 1.8 4.3
15 WHO_meaningful_bin 4.9 7.1 3.9 0.0
16 WHO_concentrate_bin 3.3 3.5 2.1 4.3
17 WHO_feel_safe_bin 1.6 2.4 1.1 0.0
18 WHO_healthy_env_bin 3.3 1.2 0.4 0.0
19 WHO_energy_bin 4.9 7.1 4.6 8.7
20 WHO_body_appear_bin 3.3 8.2 5.0 8.7
21 WHO_money_bin 13.1 25.9 14.6 17.4
22 WHO_information_bin 8.2 7.1 3.9 0.0
23 WHO_leisure_bin 1.6 8.2 4.6 8.7
24 WHO_get_around_bin 3.3 5.9 3.9 8.7
25 WHO_sleep_satisf_bin 18.0 24.7 20.4 34.8
26 WHO_ability_ADL_bin 4.9 5.9 4.3 0.0
27 WHO_capacity_work_bin 6.6 5.9 7.5 4.3
28 WHO_satisf_self_bin 3.3 7.1 5.7 8.7
29 WHO_satisf_relat_bin 3.3 12.9 4.3 8.7
30 WHO_satisf_sex_bin 21.3 22.4 21.4 17.4
31 WHO_satisf_support_bin 1.6 4.7 3.2 4.3
32 WHO_living_place_bin 6.6 7.1 2.9 13.0
33 WHO_access_health_bin 9.8 11.8 13.9 13.0
34 WHO_transport_bin 0.0 3.5 4.6 13.0
35 WHO_neg_feelings_bin 14.8 17.6 16.1 17.4